Quantitative Finance Stack Exchange
Quantitative Finance Stack Exchange

Questions tagged [black-scholes]

Black-Scholes is a mathematical model used for pricing options.

Black and Scholes first proposed the model in 1973 in a paper titled "The Pricing of Options and Corporate Liabilities".

The equation at the center of the model uses partial differential equations to calculate the price of options.

In 1997, Scholes received the Nobel Prize in Economics for his work. Black was ineligible as he died in 1995.

1165 questions
11
votes
3 answers

What are the main limitations of Black Scholes?

Pls explain and discuss these limitations, and explain which models can I use to overcome these limitations. Alternatively, provide examples of how to modify the original Black Scholes to overcome these limitations.
user322
10
votes
2 answers

Why $N(d_1)$ and $N(d_2)$ are different in Black & Scholes

I'm struggling to understand the meaning of $d_1$ and $d_2$ in Black & Scholes formula and why they're different from each other. As per the formula, $$C = SN(d_1) - e^{-rT}XN(d_2)$$ which means if the call option gets exercised, one would receive…
andreister
  • 203
  • 1
  • 6
9
votes
5 answers

Value of a European Call option with Infinite maturity

It is a job interview question. So, what's the value of a vanilla European call option of infinite maturity, and a given strike, vol, interest rate, spot price. I think, the answer should be "zero". The contract never pays, because infinite maturity…
bhutes
  • 996
  • 5
  • 13
8
votes
1 answer

Black Scholes paradox exercise

Any idea where lies the problem? Thank you for suggestions.
Michael Mark
  • 766
  • 5
  • 14
6
votes
2 answers

Trading days or calendar days for Black-Scholes parameters?

Black-Scholes requires volatility estimated in trading days. How does this affect other parameters? Specifically, should the time-to-expiration also be in trading days? And how does this affect the risk-free interest rate?
bubbly
  • 95
  • 1
  • 3
6
votes
3 answers

Deriving the Black-Scholes formula as the expected value on the payout of an option

My question concerns the Black-Scholes formula for the value of a European option, namely \begin{align} C(S_t, t) &= N(d_1)S_t - N(d_2) Ke^{-r(T - t)} \\ d_1 &= \frac{1}{\sigma\sqrt{T - t}}\left[\ln\left(\frac{S_t}{K}\right) + \left(r +…
Mike Crumley
  • 275
  • 3
  • 9
5
votes
2 answers

Black-Scholes PDE: what is the form of the boundary conditions

I'm working on the Black-Scholes equation, but I'm pretty new to financial modeling. Right now, I am trying to understand the Black-Scholes PDE. I understand that the Black-Scholes equation is given by \begin{equation*} \frac{\partial C}{\partial t}…
meraxes
  • 175
  • 1
  • 5
4
votes
0 answers

Black-Scholes PDE to heat equation, nonconstant coefficients

Can someone provide me with details or a reference on how to transform the Black-Scholes PDE with nonconstant coefficients (i.e. $r=r\left(S,t\right)$, $\sigma=\sigma\left(S,t\right)$) to the heat equation? Thank you in advance.
user5525
  • 41
  • 1
4
votes
1 answer

Call Option on the Square of a Log-Nomral Asset

I'm working on a quant interview question from the book called Quant Job Interview Questions And Answers (by Mark Joshi and other authors).I cannot understand its answer well and really appreciate your advice: Here is the question: suppose you have…
M00000001
  • 647
  • 4
  • 15
4
votes
1 answer

Option pricing with negative short-term interest rates

In countries with negative short-term risk-free interest rates, do you just use a negative "r" in the Black-Scholes formula, or do adjustments need to be made?
Fortranner
  • 592
  • 3
  • 9
4
votes
1 answer

Expectation of $\frac {S_{T_2}} {S_{T_1}}$ at $T_0$

Is my below computation correct (assuming flat volatlity Black Scholes model, flat interest rate curve): $\mathbb{E}(\frac {S_{T_2}} {S_{T_1}}| \mathcal{F}_{T_0})$ $ = \mathbb{E}{\frac{S_{T_0}e^{(r-\frac{\sigma^2}{2})T_2+\sigma…
bhutes
  • 996
  • 5
  • 13
4
votes
1 answer

Black-Scholes: If exercise probability is 0.5, should $D_2$=0?

Let's say we have option strike price equal to current stock price. And we have zero risk-free rate. In this case I assume that probability of exercise is 0.5 because chances that price will go up or down are equal. As I understand $N(D_2)$ is…
Alex Kofman
  • 141
  • 1
4
votes
2 answers

Why is the rate of change of a stock price proportional to the stock price?

When deriving the Black Scholes equation, it is usually stated "we assume the change in the stock price is": $dS=\mu S(t) dt + $random term My question is why is the change in the stock price always proportional to the stock price (ignoring the…
kotozna
  • 165
  • 4
3
votes
0 answers

Black-Scholes in Delphi

when trying to implement the Black-Scholes formula in Delphi, I've found this: http://www.espenhaug.com/black_scholes.html I've checked the results against option-price.com and found they are different. Can anyone share the code for the B&S formula…
leonardorame
  • 139
  • 2
3
votes
1 answer

Formula for variance of European call/put in Black Scholes

I have a quite basic question, but I can't find a reference with it. Recall that we can use the Black-Scholes formula to price a European call or put for a market consisting when: the underlying asset following geometric Brownian motion; the risk…
Amin
  • 133
  • 1
  • 4
1
2 3 4 5